I always found it kind of weird when people maintained active, platonic relationships with their exes, especially when they were dating someone else.
That doesn't mean I've never done it or at least tried to do it, but at the end of the day it always seems like one person is ultimately going to end up getting hurt because someone almost always still has feelings for the other person when things fall apart. I've been on both sides of that phenomenon, and it wasn't pretty.
That being said, I'm not saying it can't happen and that there aren't people who are able to work out a normal, functioning relationship even after they had been previously romantically involved. But that doesn't mean that a former couple's "past history" isn't still in the air. Just ask Prince Harry's ex-girlfriend.